The present invention relates generally to methods and apparatus for determining the displacement or location of a target and, more particularly, to heterodyne interferometers and associated interferometric methods.
Heterodyne interferometers are utilized in a variety of commercial and noncommercial applications. For example, optical heterodyne interferometers commonly measure displacement or are used in sensors to measure force, pressure or other physical quantities that create a measurable displacement in a respective transducer.
Heterodyne interferometers include a stable optical source, such as a laser, for providing coherent optical signals. The optical source can provide signals directly to the system or the optical source can be remotely located and connected to the system via optical fibers. Regardless of the location of the optical source, conventional heterodyne interferometers require coherent signals having two different frequencies. In addition, most conventional heterodyne interferometers require that the signals having the first frequency be orthogonally polarized relative to the signals having the second frequency. These heterodyne interferometers are therefore classified as polarizing interferometers. For example, the Hewlett Packard 10715 differential interferometer is a type of polarizing heterodyne interferometer as described in an article by C. Steinmetz, et al., entitled Accuracy Analysis and Improvements to the Hewlett-Packard Laser Interferometer System, SPIE 816, Interferometric Metrology, p. 79 (1987). Similarly, the Hewlett Packard 5527 Laser Position Transducer System is another type of polarizing heterodyne interferometer as described in HP product brochure No. 5964-6190 E entitled Optics and Laser Heads for Laser-Interferometer Positioning Systems (1995).
More specifically, conventional polarizing interferometers include a first laser source for providing a first beam having a first frequency and a first linear polarization and a second laser source having a second frequency and a second linear polarization that is orthogonal to the first polarization state. A polarizing interferometer also includes reference and measurement arms as well as a polarizing beamsplitter for separating the first and second beams based upon their polarization such that one of the beams is directed to the measurement arm of the interferometer, while the other beam is directed to the reference arm of the interferometer. Upon returning from the measurement and reference arms, the first and second beams are mixed by a polarization analyzer or other polarization manipulating optical elements so as to create an interference pattern. While the reference arm typically has a fixed or predetermined length, the measurement arm has a length that is defined by the position of a target. As such, as the target is displaced, the optical length of the measurement arm is accordingly altered. By measuring the phase of the resulting fringes created by the interference of the first and second beams, however, the heterodyne interferometer permits the displacement of the target to be determined.
Unfortunately, the first and second beams that are produced by the laser sources generally do not have pure linear polarization. Thus, the first beam that is substantially polarized with the electric field parallel to the plane of incidence of the interferometer beamsplitter, P-polarized, also generally has some component of electric field perpendicular to the plane of incidence, S-polarized. Likewise, the second beam that is primarily S-polarized, also generally has some P-polarization. In addition, polarizing beamsplitters are not perfect and therefore do not completely separate signals that are orthogonally polarized. See N. Bobroff, xe2x80x9cRecent Advances in Displacement Measuring Interferometryxe2x80x9d, Meas. Sci. Tech. Vol. 4, pp. 907-26 (1993). As such, while a polarizing beamsplitter generally separates the beams according to their polarization state such that S-polarized signals are directed along one path and P-polarized signals are directed along another path, imperfections in conventional polarizing beamsplitters allow at least some P-polarized signals to mix with the generally S-polarized beam and, correspondingly, permit at least some S-polarized signals to mix with the generally P-polarized beam.
The mixture of the polarization states downstream of the polarizing beamsplitter is commonly termed xe2x80x9cpolarization crosstalkxe2x80x9d. As a result of polarization crosstalk, conventional polarizing interferometers having a nonlinear error in the final phase measurement. The error is periodic with the period of one wavelength of the optical path change. Since the phases of the beams that give rise to this nonlinear error can drift, the magnitude of the error can also vary over time. In order to minimize the variations in the magnitude of the nonlinear error, some polarizing interferometers rapidly dither the reference mirror that defines the optical length of the reference arm so as to average out the periodic error. While generally effective, this technique requires the interferometer to be substantially more complex.
In addition, U.S. Pat. No. 4,693,605 to Gary E. Sommargren describes an interferometer in which mixing of the different polarization states is minimized by reducing the number of reflections in the interferometric system. While somewhat helpful, this technique appears only to reduce, but not totally solve the problems created by polarization crosstalk. In addition, an article by W. Hou, et al. entitled xe2x80x9cInvestigation and Compensation of the Nonlinearity of Heterodyne Interferometersxe2x80x9d, Precision Engineering, Vol. 12, p. 91 (1992), describes a technique for compensating for some of the nonlinear errors in the final phase measurement. While also somewhat beneficial for reducing the nonlinear errors, this technique does not compensate for all nonlinear errors and is more complex by requiring twice the usual number of photodetectors and phase-measurement channels. As such, while several techniques have been developed for reducing the polarization crosstalk of heterodyne interferometers, these techniques do not eliminate the polarization crosstalk and typically increase the complexity of the interferometric system.
Nonpolarizing heterodyne interferometers have also been developed. By avoiding the mixing of beams of different polarization states, nonpolarizing interferometers reduce or eliminate the nonlinear errors in the final phase measurement that otherwise arise as a result of polarization crosstalk. See, for example, M. Tanaka, et al. xe2x80x9cLinear Interpolation of Periodic Error in a Heterodyne Laser Interferometer at Subnanometer Levelsxe2x80x9d, IEEE Trans. Instrum. Meas., Vol. 38, No. 2, pp. 552-54 (April 1989); Jack A. Stone, et al., xe2x80x9cWavelength Shift Interferometry: Using a Dither to Improve Accuracyxe2x80x9d, Proc. of the Eleventh Annual Meeting of the American Society for Precision Engineering,xe2x80x9d pp. 357-62 (Nov. 9-14, 1996); and Chien-ming Wu, et al., xe2x80x9cHeterodyne Interferometer with Subatomic Periodic Nonlinearity,xe2x80x9d Applied Optics, Vol. 38, pp. 4089-94 (1999). Unfortunately, conventional nonpolarizing interferometers suffer from several disadvantages including increased complexity created by additional optical components that must remain accurately aligned.
In addition to problems related to polarization crosstalk, conventional heterodyne interferometers are typically limited by the requirement that the target move only in a predetermined direction of interest that the interferometer is designed to measure. As such, motion of the target in a plane orthogonal to the direction of interest typically interferes with the measurement and should be avoided. In addition, tilting of the target or the stage on which the target is mounted can adversely influence the measurement. Accordingly, conventional heterodyne interferometers generally limit the target to movement in the direction of interest and do not permit movement in a plane orthogonal to the direction of interest or tilting of the target.
A heterodyne interferometer and an associated interferometric method are provided to address the limitations of conventional heterodyne interferometers. In particular, the heterodyne interferometer of the present invention is a nonpolarizing interferometer that significantly reduces, if not eliminates, polarization crosstalk without requiring the complexity and alignment accuracy of conventional nonpolarizing interferometers. In addition, the heterodyne interferometer of one advantageous embodiment includes a measurement arm having a pair of crossed porro prisms, one of which serves as the target, and which is permitted to translate within limits set by the optical apertures in directions orthogonal to the measurement axis without adversely affecting the measurement. Similarly, this configuration allows the target porro prism to rotate about the measurement axis or either orthogonal axis within some limited range without adversely affecting the measurement. The allowable tilt range is dependent on factors such as displacement measurement tolerance, beam diameter, and design dimensions, but can be of sufficient extent as to be a determining factor in selecting this approach over conventional methods.
According to the present invention, the heterodyne interferometer includes a beamsplitter for splitting each of a first beam and a coherent second beam into at least two partial beams. In instances in which the first and second beams have the same polarization, the beamsplitter is a nonpolarizing beamsplitter. However, in instances in which the first and second beams are orthogonally polarized, the beamsplitter is a polarizing beamsplitter. Typically, the first beam and the partial first beams have a first frequency, while the second beam and the partial second beams have a second frequency. While the first and second beams can be provided in different manners, the first and second coherent beams are typically provided by a two-frequency laser or by a single-frequency laser plus frequency shifting devices.
The heterodyne interferometer also includes a reference arm and a measurement arm, downstream of the beamsplitter. The beamsplitter therefore directs a partial first beam and a partial second beam to the reference arm so as to propagate along a reference path of a predetermined length. Likewise, the beamsplitter directs another partial first beam and another partial second beam to the measurement arm so as to propagate along a measurement path. In this regard, the length of the measurement path is at least partially defined by the position of a target.
According to one advantageous aspect of the present invention, the first beam and the partial first beams propagate in a first plane, while the second beam and the partial second beams propagate in a second plane that is offset from the first plane. The first beam and the partial first beams therefore propagate in a downstream direction without spatially overlapping with the second beam and the partial second beams until transit through the measurement and reference arms is completed. As such, the polarization states of the first beam and the partial first beams and the second beam and the partial second beams do not have an opportunity to mix and, as a result, polarization crosstalk is avoided. While the first and second planes can be offset by a variety of distances sufficient to prevent spatial overlap, the first and second planes are preferably offset by at least two beam diameters.
The heterodyne interferometer can also include at least one detector downstream of the reference and measurement arms. The detector receives a partial first beam that has traversed either the reference arm or the measurement arm as well as a partial second beam that has traversed the other of the reference arm and the measurement arm. Based upon the interference fringes created by mixing the partial first beam and the partial second beam, the detector can provide a signal indicative of the displacement of the target. More typically, the heterodyne interferometer includes first and second detectors. In this embodiment, each of the detectors receives a partial first beam that has traversed one of the reference arm and a measurement arm as well as a partial second beam that has traversed the other of the reference arm and the measurement arm. Based upon the output of the first and second detectors, the displacement of the target can be accurately determined. An important practical consideration is that the measurement of the phase difference from the two detector configuration is insensitive to common mode phase shifts that result from phase variations in the delivery of the signal sources to the interferometer. Such variations can be especially significant when optical fibers are used to deliver light from the laser sources to the interferometer. If only one detector is used, the detected interference signal phase resulting from target motion is indistinguishable from either thermal or strain induced optical path length variations in the delivery optical fibers. By using two detectors, together with electronics that measure the difference of the interference signal phase from each, any phase variations that occur prior to the interferometer beamsplitter are cancelled. Thus, this phase difference measurement is sensitive only to differential optical path length variations between the measurement and reference arms. As such, the heterodyne interferometer can accurately measure the displacement of a transducer designed to measure force, pressure or other physical quantities without being adversely affected by nonlinear errors arising from polarization crosstalk.
According to one advantageous embodiment, the heterodyne interferometer has a measurement arm that includes a pair of crossed porro prisms. In this regard, at least one of the porro prisms is adapted to move in conjunction with the target to thereby at least partially define the length of the measurement path. By utilizing the pair of crossed porro prisms, the heterodyne interferometer of this advantageous embodiment permits the target to translate to a limited extent in a direction orthogonal to the measurement path without adversely affecting the measurements obtained by the heterodyne interferometer. In addition, the pair of crossed porro prisms permits the target to be tilted to a limited extent without adversely affecting the measurements provided by the heterodyne interferometer. Thus, the heterodyne interferometer of this advantageous embodiment is relatively immune to movement of the target in directions other than the direction of interest in order to further improve the reliability of the measurements obtained by the heterodyne interferometer and associated interferometric method of the present invention.